The production of isolated high-energy photons accompanied by jets has been measured in deep inelastic ep scattering with the ZEUS detector at HERA, using an integrated luminosity of 326 pb−1. Measurements were made for exchanged photon virtualities, Q2, in the range 10 to 350 GeV2. The photons were measured in the transverse-energy and pseudorapidity ranges 4<ETγ<15 GeV and −0.7<ηγ<0.9, and the jets were measured in the transverse-energy and pseudorapidity ranges 2.5<ETjet<35 GeV and −1.5<ηjet<1.8. Differential cross sections are presented as functions of these quantities. Perturbative QCD predictions give a reasonable description of the shape of the measured cross sections over most of the kinematic range, but the absolute normalisation is typically in disagreement by 20–30%.